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Derandomization of Dimensionality Reduction and SDP Based Algorithms

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Algorithms and Data Structures (WADS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3608))

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Abstract

We present two results on derandomization of randomized algorithms. The first result is a derandomization of the Johnson-Lindenstrauss (JL) lemma based randomized dimensionality reduction algorithm. Our algorithm is simpler and faster than known algorithms. It is based on deriving a pessimistic estimator of the probability of failure. The second result is a general technique for derandomizing semidefinite programming (SDP) based approximation algorithms. We apply this technique to the randomized algorithm for Max Cut. Once again the algorithm is faster than known deterministic algorithms for the same approximation ratio. For this problem we present a technique to approximate probabilities with bounded error.

Supported by NSF Grant CCR-0311321.

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References

  1. Achlioptas, D.: Database-Friendly Random Projections. In: Proceedings of the 20th ACM Symposium on Principles of Database Systems, pp. 274–281 (2001)

    Google Scholar 

  2. Alon, N., Kahale, N.: Approximating the Independence Number via the θ-Function. Mathematical Programming 80(3), 253–264 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. Alon, N., Spencer, J.H.: The Probabilistic Method. Wiley Inter-science Series in Discrete Mathematics and Optimization (1991)

    Google Scholar 

  4. Arriaga, R.I., Vempala, S.: An Algorithmic Theory of Learning: Robust Concepts and Random Projection. In: Proceedings of the 40th IEEE Symposium on Foundations of Computer Science, pp. 616–623 (1999)

    Google Scholar 

  5. Berger, B.: The Fourth Moment Method. In: Proceedings of the 2nd Annual ACM SIAM Symposium on Discrete Algorithms, pp. 373–383 (1991)

    Google Scholar 

  6. Bourgain, J.: On Lipschitz Embedding of Finite Metric Spaces in Hilbert Space. Israeli Journal of Mathematics 52, 46–52 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  7. Dasgupta, S., Gupta, A.: An Elementary Proof of a Theorem of Johnson and Lindenstrauss. Random Structures and Algorithms 22(1), 60–65 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Engebretsen, L., Indyk, P., O’Donnell, R.: Derandomized Dimensionality Reduction with Applications. In: Proceedings of the 13th Annual ACM SIAM Symposium on Discrete Algorithms, pp. 705–712 (2002)

    Google Scholar 

  9. Feller, W.: An Introduction to Probability Theory and its Applications, volumes 1 & 2, 3rd ed., Wiley Series in Probability and Mathematical Statistics (1970)

    Google Scholar 

  10. Frankl, P., Maehara, H.: The Johnson-Lindenstrauss Lemma and the Sphericity of Some Graphs. Journal of Combinatorial Theory Series A 44(3), 355–362 (1987)

    MathSciNet  Google Scholar 

  11. Frieze, A., Jerrum, M.: Improved Approximation Algorithms for Max k-Cut and Max Bisection. In: Proceedings of the 3rd International Conference on Integer Programming and Combinatorial Optimization, pp. 1–13 (1995)

    Google Scholar 

  12. Goemans, M., Williamson, D.: 0.878 Approximation Algorithms for MAX CUT and MAX 2SAT. In: Proceedings of the 26th Annual Symposium on the Theory of Computing, pp. 422–431 (1994)

    Google Scholar 

  13. Indyk, P., Motwani, R.: Approximate Nearest Neighbors: Towards Removing the Curse of Dimensionality. In: Proceedings of the 30th Annual Symposium on the Theory of Computing, pp. 604–613 (1998)

    Google Scholar 

  14. Johnson, W.B., Lindenstrauss, J.: Extensions of Lipschitz Mappings into Hilbert Space. Contemporary Mathematics 26, 189–206 (1984)

    MATH  MathSciNet  Google Scholar 

  15. Karger, D., Motwani, R., Sudan, M.: Approximate Graph Coloring by Semidefinite Programming. In: Proceedings of the 35th IEEE Symposium on Foundations of Computer Science, pp. 1–10 (1994)

    Google Scholar 

  16. Linial, N., London, E., Rabinovich, Y.: The Geometry of Graphs and Some of its Algorithmic Applications. In: Proceedings of the 35th IEEE Symposium on Foundations of Computer Science, pp. 577–591 (1994)

    Google Scholar 

  17. Mahajan, S., Ramesh, H.: Derandomizing Semidefinite Programming Based Approximation Algorithms. In: Proceedings of the 36th IEEE Symposium on Foundations of Computer Science, pp. 162–169 (1995)

    Google Scholar 

  18. Milman, V.D., Schechtman, G.: Asymptotic Theory of Finite Dimensional Spaces. Lecture Notes in Mathematics. Springer, Heidelberg (1980)

    Google Scholar 

  19. Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, Cambridge (1995)

    MATH  Google Scholar 

  20. Pan, V.Y.: Solving a Polynomial Equation: Some History and Recent Progress. SIAM Review 39(2), 187–220 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  21. Raghavan, P.: Probabilistic Construction of Deterministic Algorithms: Approximating Packing Integer Problems. Journal of Computer and System Sciences 37, 130–143 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  22. Raghavan, P., Thompson, C.D.: Randomized Rounding: A Technique for Provably Algorithms and Algorithmic Proofs. Combinatorica 7, 365–374 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  23. Sivakumar, D.: Algorithmic Derandomization via Complexity Theory. In: Proceedings of the 34th Annual Symposium on the Theory of Computing, pp. 619–626 (2002)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, Johns Hopkins University, Baltimore, MD, 21218

    Ankur Bhargava & S. Rao Kosaraju

Authors
  1. Ankur Bhargava
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  2. S. Rao Kosaraju
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Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Cheriton School of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ont., Canada

    Alejandro López-Ortiz

  3. School of Computer Science, Carleton University, 1125 Colonel By Drive, K1S 5B6, Ottawa, Canada

    Jörg-Rüdiger Sack

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© 2005 Springer-Verlag Berlin Heidelberg

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Bhargava, A., Kosaraju, S.R. (2005). Derandomization of Dimensionality Reduction and SDP Based Algorithms. In: Dehne, F., López-Ortiz, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2005. Lecture Notes in Computer Science, vol 3608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11534273_35

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  • DOI: https://doi.org/10.1007/11534273_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28101-6

  • Online ISBN: 978-3-540-31711-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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